Modeling and identification of the electrohysterographic
volume conductor by high-density electrodes
Citation for published version (APA):
Rabotti, C., Mischi, M., Beulen, L., Oei, S. G., & Bergmans, J. W. M. (2010). Modeling and identification of the electrohysterographic volume conductor by high-density electrodes. IEEE Transactions on Biomedical
Engineering, 57(3), 519-527. https://doi.org/10.1109/TBME.2009.2035440
DOI:
10.1109/TBME.2009.2035440
Document status and date: Published: 01/01/2010
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Modeling and Identification of the
Electrohysterographic Volume Conductor
by High-Density Electrodes
Chiara Rabotti*, Massimo Mischi, Lean Beulen, Guid Oei, and Jan W. M. Bergmans, Senior Member, IEEE
Abstract—The surface electrohysterographic (EHG) signal rep-resents the bioelectrical activity that triggers the mechanical con-traction of the uterine muscle. Previous work demonstrated the relevance of the EHG signal analysis for fetal and maternal moni-toring as well as for prognosis of preterm labor. However, for the introduction in the clinical practice of diagnostic and prognostic EHG techniques, further insights are needed on the properties of the uterine electrical activation and its propagation through bio-logical tissues. An important contribution for studying these phe-nomena in humans can be provided by mathematical modeling. A five-parameter analytical model of the EHG volume conductor and the cellular action potential (AP) is proposed here and tested on EHG signals recorded by a grid of 64 high-density electrodes. The model parameters are identified by a least-squares optimization method that uses a subset of electrodes. The parameters repre-senting fat and abdominal muscle thickness are also measured by echography. The mean correlation coefficient and standard devia-tion of the difference between the echographic and EHG estimates were 0.94 and 1.9 mm, respectively. No bias was present. These re-sults suggest that the model provides an accurate description of the EHG AP and the volume conductor, with promising perspectives for future applications.
Index Terms—Action potential, electrohysterography, high-density (HD) electrodes, parameter estimation, smooth muscle, subcutaneous tissue thickness, volume conductor.
I. INTRODUCTION
T
HE SEQUENCE of contraction and relaxation of the uter-ine muscle (myometrium) results from the cyclic depolar-ization and repolardepolar-ization of the muscle–cell membranes [1]. The spontaneous electrical activity of the myometrium, which can initiate in any cell (pacemaker) and then excites surrounding regions, consists of bursts of action potentials that can be mea-sured at the abdominal surface (electrohysterogram) [2], [3]. Uterine contractions are often the first sign of labor; therefore, when occurring preterm, they need to be promptly suppressed by tocolytics. Instead, during labor, a coordinated and stronguter-Manuscript received May 20, 2009; revised August 27, 2009. First published October 30, 2009; current version published February 17, 2010. This work was supported by Dutch Technology Foundation STW. Asterisk indicates
corre-sponding author.
*C. Rabotti is with the Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven 5600MB, The Netherlands (e-mail: c.rabotti@tue.nl).
M. Mischi and J. W. M. Bergmans are with the Department of Electrical Engineering, Eindhoven University of Technology, Eindhoven 5600MB, The Netherlands (e-mail: m.mischi@tue.nl; j.w.m.bergmans@tue.nl).
L. Beulen and G. Oei are with the Department of Obstetrics and Gynecol-ogy, M´axima Medical Center, Veldhoven 5500MB, The Netherlands (e-mail: leanbeulen@gmail.com; g.oei@mmc.nl).
Digital Object Identifier 10.1109/TBME.2009.2035440
ine activity is required for the effective expulsion of the fetus at the end of delivery. Accurate monitoring of the uterine activity is therefore essential. The methods currently employed in clini-cal practice for uterine activity monitoring, such as internal and external tocographies, cervical change evaluation by digital or ultrasound examination, and the measurements of biomarkers (e.g., fibronectine) in symptomatic women, could support the selection of patients at higher risk of preterm delivery within few days, but they are either invasive or not sufficiently accu-rate for effective prognosis and, therefore, prompt treatment of premature birth [4]–[6].
During a contraction, the electrohysterographic (EHG) sig-nal can be recorded noninvasively by standard Ag–AgCl contact electrodes placed on the abdomen. Many studies demonstrated that the analysis of the EHG signal may play a key role for accurate monitoring of the uterine contractions, prediction of labor, and improvement of perinatal outcome [7]–[11]. How-ever, many issues related to the conduction pattern of electrical activation are still unsolved [12].
An important contribution for studying noninvasively the con-duction properties of EHG signals and the development of novel monitoring technology can be provided by modeling techniques. At the myometrium level, the cellular action potential (AP) generation and the excitation–contraction coupling have been recently accurately modeled as a function of a large number of electrophysiological parameters related to ionic concentra-tions [13], [14]. Instead, the myometrium-skin volume conduc-tor has been only partially investigated, and it is typically con-sidered as a homogeneous infinite layer [13], [15]. As a result, the myometrium-skin conduction properties are assumed only dependent on the distance between source and recording site. Nevertheless, a complete understanding of the volume conduc-tor effect on the measured signals is fundamental to support the development of accurate prognostic and diagnostic tools based on the EHG signal analysis.
In this study, a myometrium-skin conduction model is devel-oped that consists of a four-layer model obtained by extension of simulation studies reported in the literature for the skeletal elec-tromyogram [16]. The volume conductor effect is formalized in the spatial frequency domain by a transfer function that accounts for the physical and geometrical properties of the biological tis-sues interposed between the source of electrical current in the myometrium and the recording site on the skin. The intracellular AP is mathematically modeled by a Gamma probability density function [17]. After model reduction, the potential recorded on the skin surface depends on five parameters, of which three are
520 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 3, MARCH 2010
related to the source signal shape and two are given by the thick-ness of the fat and the abdominal muscle. The model parameters are estimated from EHG measurements performed by a grid of 64 high-density (HD) electrodes on five pregnant women at term with uterine contractions. For comparison, the values of fat and abdominal muscle thickness were also measured by echography.
II. METHODOLOGY
A. Background
The contractile element of the uterus is the myometrium, which is composed of billions of smooth muscle cells. The sequence of contraction and relaxation results from a cyclic depolarization and repolarization of the muscle cells in the form of APs. The intracellular AP results from time-dependent changes in the membrane ionic permeability caused by hor-monal changes or cell-to-cell excitation. Due to changes in the permeability, ions diffuse across the membrane according to their electrochemical gradients and a transmembrane ionic cur-rent is established. APs occur in bursts; they arise in cells that act as pacemakers and propagate from cell to cell through gap junctions, which are low-resistance electrical connections [2]. It has been shown that gap junctions are present between my-ometrial cells in pregnant animals only during parturition [18]. Due to a lack of evidence [19], many authors concluded that no classical linear propagation of single APs, similar to the myocardium, could be assumed for the myometrium, and that only a global propagation of the whole burst envelop could be measured [19], [20]. However, more recently, extensive mea-surements of the electrical activity of the guinea pig uterus us-ing a grid of extracellular electrodes clearly demonstrated that also for the myometrium, similarly to the myocardium, a lin-ear propagation of single electrical spikes occurs and can be measured [12], [21], [22].
In this study, the potential recorded on the skin surface is for-malized as a function of the transmembrane ionic current and the properties of the volume conductor between the myometrium and the skin. For identifying the model parameters, single sur-face APs are visually selected from the bursts recorded during contractions. We assume that, below the recording electrodes, the current source can be approximated by a planar wave that propagates, as hypothesized in [13], either along the longitudinal or the circumferential axis of the uterus.
B. System Modeling
1) Volume Conductor Modeling: The biological tissues
in-terposed between the electrical source at the myometrium and the recording site on the skin act as a volume conductor, pro-ducing a spatial low-pass filtering effect. Similarly to the study reported in [16] for skeletal muscles, the volume conductor be-tween the myometrium and the skin is considered as made of parallel interfaces separating the tissue layers. As the abdom-inal curvature is negligible in a limited region, the interfaces can locally be approximated by infinite parallel planes. The bi-ological tissues involved in the conduction of EHG signals are represented in Fig. 1 and consist of myometrial tissue [see (a)
Fig. 1. Schematic description of the biological tissue layers involved in the volume conductor of EHG signals.
in Fig. 1], where the source is placed at a depth y = y0, a ∆hb
thick abdominal muscle layer [see (b) in Fig. 1], a ∆hcthick fat
layer [see (c) in Fig. 1], and a ∆hd thick skin layer [see (d) in
Fig. 1].
The general relation between the potential and the current density source in a nonhomogeneous and anisotropic layer is expressed by the Poisson equation [23] as
− ∂ ∂x σx ∂φ(x, y, z) ∂x − ∂ ∂y σy ∂φ(x, y, z) ∂y + − ∂ ∂z σz ∂φ(x, y, z) ∂z = IV (x, y, z) (1)
where IV(x, y, z) is the volume current source (in amperes×
cubic meter inverse), φ(x, y, z) is the potential (in volts), and σx, σy, and σz(siemens per meter) are the conductivities of the
medium in the x-, y-, and z-directions, respectively.
Skin, fat, and myometrial tissue can be considered isotropic, i.e., the value of conductivity does not depend on the direction of propagation, and therefore, σx = σy = σz = σ, while the
ab-dominal muscle is anisotropic, i.e., σx = σxb = σz = σz b[16].
In the y-direction, σy = σy b = σxb if the muscle fiber
orienta-tion is parallel to the z-axis, and σy b = σz bif it is parallel to the
x-axis. All the tissues can be regarded as homogeneous. In the myometrium, the relation in (1) becomes
−σa ∂2 ∂x2 + ∂2 ∂y2 + ∂2 ∂z2 φa(x, y, z) = IV(x, y0, z)δ(y− y0) (2) with φa(x, y, z) and σabeing the potential and the conductivity,
and IV(x, y, z) the current source at depth y0.
All the other layers contain no current source. In the anisotropic muscle layer b, we have
σxb ∂2 ∂x2 + σy b ∂2 ∂y2 + σz b ∂2 ∂z2 φb(x, y, z) = 0 (3)
where φb(x, y, z) is the potential in this layer. In the isotropic
fat layer c, with potential φc(x, y, z), and similarly in the layers
d and e, with potentials φd(x, y, z) and φe(x, y, z), respectively,
relations of the form ∂2 ∂x2 + ∂2 ∂y2 + ∂2 ∂z2 φc(x, y, z) = 0 (4)
hold. The solution of (2)–(4) can be obtained in the spatial frequency domain by calculating the 2-D Fourier transform in the x- and z-directions. Indicating by kx and kz the spatial
angular frequencies in the x- and z-directions, due to the Fourier transform properties, the second derivatives in the x- and z-directions become, in the spatial frequency domain,−kx2 and
−kz2, respectively, by multiplications. Furthermore, we define
ky = k2 x+ k2z and ky b = σy b σxb k2 x+ σz b σxb k2 z.
Therefore, indicating by Φa, Φb, and Φc the Fourier transform
of the potentials φa, φb, and φc, respectively, in the spatial
frequency domain, (2)–(4) become ∂2 ∂y2 − k 2 y Φa(kx, y, kz) = IV(kx, y, kz) σa δ(y− y0) (5) ∂2 ∂y2 − k 2 y b Φb(kx, y, kz) = 0 (6) ∂2 ∂y2 − k 2 y Φc(kx, y, kz) = 0 (7)
respectively. Equations of the same form as (7), which refers to layer c, also hold for the skin layer, d, and the air, e. In order to obtain the expression of the potential on the skin surface, all the obtained partial differential equations can be solved by adding the boundary conditions at the four interfaces, namely the continuity of the current in the y-direction, the continuity of the electrical field in the z- and x-directions, and the decay to zero of the potential for y→ ±∞.
The expression of the potential Φe(kx, y, kz) in the spatial
frequency domain on the skin surface (y = h3) as a function of
the current source IV = IV(kx, y0, kz) and the volume
conduc-tor properties can then be derived as given in (8), as shown at the bottom of this page, using the following conventions:
1) Ra= σa/σxb; 2) Rb = σz b/σxb; 3) Rc= σc/σxb; 4) Rd = σd/σc; 5) α1(kx, kz) = kycosh(∆hbky b)Ra+ ky bsinh(∆hbky b); 6) α2(kx, kz) = kysinh(∆hbky b)Ra+ ky bcosh(∆hbky b).
In the following, the expression of the surface potential, which has been formalized in two dimensions for completeness, is simplified and addressed as a one-dimension problem. Due to the planar wave assumption, the use of a two-dimension model is not expected to provide additional relevant information. The z-axis is considered the main component (horizontal or vertical) of the electrical activity propagation velocity. The spatial angular frequency in the x-direction, kx, is set to zero and a single line
Fig. 2. (a) Example of intracellular AP and (b) volume current source modeled in the space domain by a Gamma probability density function and its third derivative, respectively. The IAP propagation direction is parallel and opposite to the z-axis. Assuming a propagation velocity of about 10 cm/s, the depicted example corresponds to an AP duration of 150 ms.
(row or column) of the electrode grid is employed to identify the model parameters. In this respect, the use of a two-dimension grid for the acquisition is exploited to single out, on the basis of the signal quality and the direction of the electrical activity propagation, the line that is used as reference for the model identification.
2) Source Modeling: Microelectrode recordings of uterine
electrical activity showed that the uterine intracellular AP, sim-ilarly to skeletal muscles, is characterized, on time, by a fast depolarization followed by a reversal of membrane polarity and a slower repolarization [24]. In the considered direction, z, the intracellular AP appearance in the time domain, t, is converted to the space domain by assuming a constant intracellular AP propagation velocity component in the z-direction, vz, using
the relation
z =−vzt. (9)
As also suggested for skeletal muscles [17], the intracellular AP (IAP) at the myometrium, IAP(z), can be suitably described in the space domain by a function that has the shape of a Gamma probability density function
IAP(z) = zα−1e−z/β βαΓ(α) , z≥ 0 0, z < 0 (10)
where Γ is the Gamma operator, α∈ R+ is a dimensionless shape parameter, and β∈ R+ is a spatial scale parameter.
The example of the function IAP(z) modeled by (10) in Fig. 2(a) refers to a propagation velocity vz, parallel and
op-posite to the z-axis. Considered the relation in (9) between the
Φe(kx, h3, kz) = (1− Rd){ky bα1(kx, kz) cosh[(∆hc− ∆hd)ky]− Rckyα2(kx, kz) sinh[(∆hc− ∆hd)ky]} 2ekyy0I V(kx, y0, kz)ky b/σxb +(1 + Rd){ky bα1(kx, kz) cosh[(∆hc+ ∆hd)ky] + Rckyα2(kx, kz) sinh[(∆hc+ ∆hd)ky]} 2ekyy0I V(kx, y0, kz)ky b/σxb −1 (8)
522 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 3, MARCH 2010
spatial and temporal properties of a waveform, when compared to the intracellular APs depicted in the literature [24], [25], the shape of the modeled AP in Fig. 2(a) represents of microelec-trode recordings of uterine activity.
As from (1), the source of our model, IV, is a volume current
source density; being a measure of the current outflow per unit volume, IV can then be obtained by the divergence of the current
density J (x, y, z), in amperes per meter square, i.e.,
IV =∇ · J(x, y, z) =
∂
∂z(J (z)) (11)
where the last equality results from the hypothesis of a single propagation direction along z. Assuming the core-conductor model [23], the transmembrane ionic current density J (z) is proportional to the second spatial derivative of the IAP profile [23]. In the spatial frequency domain, the volume current source IV(kz) of the model in (8) is therefore given as
IV(kz) = F A∂ 3IAP(z) ∂z3 = Aik3z −ikz+1β −α β−α √ 2π (12) where F indicates the Fourier transform, A is an amplitude scal-ing factor that accounts for the number of cells simultaneously active during the contraction, and i =√−1.
3) Model Reduction: The surface potential φe(kx, h3, kz)
in (8) depends on the tissue thicknesses and conductivities, the source depth y0, and the parameters α, β, and A in (12). The
tis-sue conductivities are, however, relatively invariant and the val-ues reported in the literature are used [26]–[28]. For APs prop-agating in the direction parallel to the abdominal muscle fiber orientation, i.e., z parallel to the vertical line of the abdomen, by assuming a uterine conductivity σa= 0.2 S· m−1 [26] and
a transversal muscle conductivity σxb = 0.09 S· m−1 [27], we
obtain Ra = 2.2, Rb = 5, Rc= 0.5, and Rd = 20 [28]. For
APs propagating horizontally, σxb is the longitudinal
abdom-inal muscle conductivity; therefore, σxb = 0.4 S· m−1 [27],
Ra= 0.5, Rb = 0.2, and Rc= 0.225.
A further reduction of the model parameter number is ob-tained by setting the skin tissue thickness, ∆hd, to a
con-stant value. A low intersubject variability of the skin thickness, demonstrated already in previous studies [29], is also suggested by 15 echographic measurements performed at the M´axima Medical Center, Veldhoven, The Netherlands, from 12 pregnant and three nonpregnant women. In agreement with the values employed in other modeling approaches [28] and those mea-sured for dermatological investigations on the abdomen [29], we measured a skin thickness equal to 2 mm in 87% of the cases. Therefore, the model is identified by assuming a constant skin thickness ∆hd = 2 mm.
An additional model reduction also concerns the source depth y0. Assuming the source to be close to the
myometrium-abdominal muscle interface, y0 → 0 and, therefore, the
expo-nential term in (8) can be approximated by a McLaurin expan-sion ekyy0 → 1.
Fig. 3. Schematic description of the sensor placement.
C. Experimental Data Recording and Preprocessing
The measurements were performed at the M´axima Medical Center after approval by the ethical committee of the hospital. Five women in labor, admitted to the hospital with contractions, were enrolled in the study after signing an informed consent. The sensors were placed as described in Fig. 3 after skin preparation for contact impedance reduction. The EHG was recorded using a Refa system (TMS International, Enschede, The Netherlands), comprising a multichannel amplifier for electrophysiological signals and a grid of 64 (8× 8) HD electrodes (1 mm diameter, 4 mm interelectrode distance). The sampling frequency was 1024 Hz. The electrodes have a flexible support, which can be fixed to the skin by a double-sided adhesive tape mask that covers the interelectrode space and leaves the sensing surface recessed in a cavity. The cavity can be filled by electrolyte gel. The combined use of flexible and recessed electrodes contributes to the reduction of movement artifacts [30].
The HD electrode grid was placed on the midline of the lower abdomen immediately below the umbilicus. By analyzing a set of previous measurement performed with electrodes distributed on the abdomen, the signals recorded by electrodes placed in this region resulted less affected by movement artifacts, such as respiration, than the signals recorded by electrodes placed in other locations [31]. The common reference for the monopolar EHG signals recorded by the HD electrode was placed on the right hip, close to the ground (GRD) electrode. The external tocogram, simultaneously recorded due to medical prescription, was employed to support the assessment of the contraction pe-riod. An accelerometer was fixed on the HD electrodes to detect movements and exclude from the analysis signal segments af-fected by motion artifacts. An Aloka ultrasound scanner was employed to measure the thickness of the fat and the abdominal muscle layers underneath the HD electrode. Two echographic images were recorded: one during the quiescent period and one at the contraction peak. The values of thickness were then mea-sured on the echographic image by two independent observers. The uterine EHG signal can be affected by various noise sources, e.g., electrocardiographic (ECG) signals, electromyo-graphic (EMG) interference generated by the contraction of abdominal muscles, and different motion artifacts. It has been
Fig. 4. Example of preprocessed EHG signal recorded during labor (39 week of gestation) and effect of filtering in two different frequency bands.
extensively reported that the EHG signal does not have significant frequency components outside the frequency band 0.1–5 Hz [20]. The interference due to the EMG signal has a dominant frequency component of about 30 Hz [8], the main frequency of respiration is up to 0.34 Hz, and the lower frequency of the ECG signal is given by the heart rate, which can be as low as 1 Hz [32]. In the literature, either narrow bandpass filtering (i.e., between 0.34 and 1 Hz) [10] or maternal ECG subtraction combined with bandpass filtering between 0.1 and 3 Hz was proposed to improve the EHG SNR [11]. In this paper, a sixth-order Butterworth bandpass filter with cut-off frequencies at 0.1 and 0.8 Hz is used. The example of AP in Fig. 4, filtered be-tween 0.1 and 5 Hz and bebe-tween 0.1 and 0.8 Hz, in fact, suggests that low-pass filtering below 0.8 Hz does not affect the signal shape while removing the ECG interference at the heart rate. Due to the electrode typology and position, low-frequency oscilla-tions due to the respiration are not visible in the recorded signals.
D. Model Parameter Identification
For each woman, two different signal time segments, each containing a propagating (i.e., it shows a delay between consec-utive channels) surface AP, were visually selected on the pre-processed signal and used as reference for validation by mean square estimation of the model parameters.
Since possible artifacts, such as those due to ECG and move-ments, do not propagate along the electrode grid, the surface APs in the different channels represent the same AP propagat-ing below the electrodes. We assume that the conduction wave can be approximated by a planar wave. Due to the planar wave assumption, the spatiotemporal information of the surface AP recorded by one column and one row of the electrode grid is representative of the AP propagation. The best row and col-umn are then selected using the similarity among the recorded signals as quality index. A high interchannel signal similarity, in fact, provides a first evidence that the selected electrodes are recording APs originating from a single source. Furthermore, as we assume that the AP propagates either vertically or horizon-tally [13], we single out the line (either the column or the raw) that is parallel to the AP direction of propagation, estimated by analysis of the AP conduction velocity. In fact, no spatial in-formation could be derived from the electrodes that are aligned
orthogonally to the AP propagation direction. Note that, due to the preliminary line selection based on the interchannel signal similarity, the conduction velocity estimates in the selected line are more reliable [33].
Possible indexes of the shape similarity between two signals are the correlation coefficient and the coherence spectrum [34]. Differently from the correlation coefficient, the similarity index provided by the coherence spectrum, which is the frequency equivalent of the correlation coefficient, is independent of the signal phase, and therefore, does not require preliminary sig-nal alignment. The coherence spectrum is therefore calculated for all the couples of signals in a line and the median value considered as line signal quality index.
For assessing the surface AP conduction velocity between two electrodes, the phase-difference method is employed [35]. The conduction velocity is calculated between all the possible couples of channels in the considered lines. A more robust es-timation of the delay can then be obtained by exploiting the redundancy of this information and taking the median value of the delay estimates.
Once a channel line is identified on the basis of coherence and propagation, the eight-channel-surface APs in the time do-main are used for identification of the model parameters in the space domain. However, due to the wavelength of the uterine AP and the spatial low-pass filtering effect of the biological tissues interposed between the myometrium and the skin, the signal simultaneously recorded by the eight electrodes may not provide enough spatial information for reconstructing a com-plete surface AP in the space domain. After calculation of the surface AP conduction velocity, assumed to be constant, time information is used to recover the missing spatial information. Eventually, the surface AP, SAP(z), is represented by 16 spatial samples (see Fig. 8).
The parameters of the model in (8) and (11) are identified on simulated and real signals by minimization of the mean error e, which is given by e = N z = 1 (SAP(z)− SAPM(z))2 N (13)
between the measured (simulated) reference signal SAP(z) and the modeled potential SAPM(z) = F−1{φe(kz)}. The Nelder–
Mead simplex search method is used for the minimization of e, which is given for SAPM = SAPM [36]. For the minimization
of e, the values of the abdominal fat and muscle thickness are initialized at 19 and 12 mm, respectively; for the considered abdominal tissues, these are the mean values reported in the literature for young women [37].
III. RESULTS
A. Simulation Results
Simulated surface APs were obtained for all the possible combinations of realistic values of ∆hb and ∆hc, and for a
fixed set of source parameters. Ten values of abdominal muscle thickness, ∆hb, and fat tissue thickness, ∆hc, between 1 and
524 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 3, MARCH 2010
Fig. 5. (a) Standard deviation of the fat thickness estimates, SDc, and (b) standard deviation of the abdominal muscle thickness estimates, SDb, over 50 simulated
surface APs with SNR = 12dB. The plots show the results (gray level) as a function of the tissue-thickness values adopted for the surface AP simulation.
Fig. 6. (A) Measured and estimated values of fat tissue thickness and (b) abdominal muscle thickness.
16 mm and between 1 and 30 mm, respectively, were considered for the simulations [37]. Gaussian white noise was added to each of the simulated surface AP. The noise power was estimated as the mean squared error between SAP and SAPM obtained by the
model identification on the real signals. Each noisy simulated surface AP was used as reference to obtain an estimate of the fat thickness, ∆hc, and the abdominal muscle thickness, ∆hb,
as described in Section II-D.
The standard deviation, SDb, of the abdominal muscle
thick-ness estimates and the standard deviation, SDc, of the fat tissue
thickness estimates were calculated over 50 noise sequences. The standard deviation of the fat and abdominal muscle thick-ness estimates in Fig. 5(a) and (b) refers to the worst case SNR, i.e., SNR = 12 dB. In these simulations, vertical propagation was assumed, i.e., the abdominal muscle conductivity in the z-direction σz b is the longitudinal conductivity and σxb is the
transversal one. The estimates are unbiased. Fig. 5(a) shows that for ∆hb > 1 mm, SDc< 1.5 mm. As for the standard deviation
of the abdominal muscle estimates, see Fig. 5(b), for ∆hb > 1
mm, SDb < 4 mm. In the simulations reported in Fig. 5(a) and
(b), the standard deviation of the abdominal muscle thickness estimates is, in general, higher than the fat thickness. For a sim-ulated vertical propagation, this tendency is also present when higher values of SNR are considered, and it is due to the convex-ity of the error function, which is slightly higher in the direction of ∆hcthan in the direction of ∆hb. When horizontal
propaga-tion is simulated, the surface AP is more sensitive to variapropaga-tions
of the abdominal muscle thickness and the estimation of ∆hb
becomes more accurate than ∆hc.
B. Measurement Results
For each patient, the abdominal muscle and the fat layer thickness were measured by echography by two independent observers and the model parameters identified on two different time segments of the EHG signal. The values of tissue thickness recorded by echography and those estimated from the EHG sig-nal using the volume conductor model are shown in Fig. 6 for each analyzed patient. In Fig. 6, the echographic measurements refer to the contraction period and are reported in terms of inter-observer mean and standard deviation. The difference between the values of tissue thickness recorded by echography during the quiescent period and contraction (not reported in the figure) was 0.11± 0.67 mm for the fat tissue and −0.23 ± 0.34 mm for the abdominal muscle. For comparison, Fig. 6 also shows the mean and standard deviation of the parameters estimated from the surface APs.
As from the table in Fig. 6, the mean values of thick-ness measured echographically by the two observers were ∆hc= 11.32± 6.17 mm and ∆hb = 9.36± 3.63 mm,
respec-tively. The mean difference between the echographic and the electrophysiological estimates was ∆c= 0.97± 1.99 mm for
the fat and ∆b =−1.02 ± 1.21 mm for the abdominal muscle.
Fig. 7. Mean estimated values of (a) fat and (b) abdominal muscle thickness, and zero-intercept trend line as a function of the mean values measured on the echographic image.
Fig. 8. Example of recorded and modeled surface AP.
estimates, i.e., with no distinction between the two different tis-sues, was 0.02± 1.9 mm.
The variability between the two types of measurements was comparable, with a mean interobserver variability of 1.1 mm by echography and a mean difference between the tissue thickness estimated by the two surface APs of 1.2 mm.
In Fig. 7, the estimated values of tissue thicknesses are plotted against the values measured by echography. By operating a lin-ear regression of the data with the hypothesis of zero intercept, we obtained correlation coefficients R = 0.9458(p < 0.05) and R = 0.9342(p < 0.05) for the fat tissue and the abdominal mus-cle tissue, respectively. The angular coefficient of the regression lines is 1.03 and 0.89 for the fat tissue and the abdominal muscle, respectively.
On average, we obtained values of the error as e = 4.8× 10−3± 3.4 × 10−3 mV. Fig. 8 shows an average example of model fit (e = 4.19× 10−3mV).
IV. DISCUSSION ANDCONCLUSION
In this paper, we propose a four-layer mathematical model of the conduction of EHG signals from the myometrium to the skin surface. The shape of the cellular AP is modeled by a Gamma probability density function. Based on physiological and experimental observations, the number of model parameters can be reduced. The model is then identified from the EHG signal recorded on women in labor by surface electrodes. Of the five estimated parameters, two can also be measured by ecography. The model can therefore be reliably validated by comparison with the echographic measurements [38].
The model was tested on ten segments of EHG signals recorded on five women in labor. On average, the parameters estimated using the model differed from the ones measured by
echography by less than 1 mm for the fat tissue and 1.2 mm for the abdominal muscle tissue. The good agreement between the measured and estimated parameters was also confirmed by their high correlation (R = 0.9458 and R = 0.9342).
On the experimental data, the estimation accuracy of the fat thickness was comparable to that of the abdominal muscle thick-ness. On simulated signals, the error between the measured and estimated surface APs resulted more sensitive to the abdom-inal muscle or the fat tissue thickness error, depending on the considered direction of propagation (vertical or horizontal). This dependency between the estimate accuracy and the AP direction of propagation is likely to be related to the anisotropy of the ab-dominal muscle. The comparable parameter errors obtained on real data for the two different biological tissues can therefore be explained by the comparable number of selected surface AP propagating horizontally (four) with respect to those propagat-ing vertically (six).
For each woman, the tissue thickness was echographically measured by two observers and estimated on two different seg-ments of the EHG signal. The interobserver variability of the echographic measurements was comparable to the variability between the tissue values estimated by analysis of two surface APs; both variabilities resulted to be slightly higher than the mean difference between the two methods. In general, our sim-ulations show that even considering the worst realistic value of SNR, the standard deviation of the parameter estimates is modest for any realistic values of tissue thickness.
The tissue thickness was measured twice in the same location: during contraction and during the quiescent period. For the val-idation of the model, the reference values were those obtained during contraction since APs are present only during the con-traction period. According to our echographic measurements, a decrease in the fat tissue and an increase in the abdominal muscle tissue thickness is observed when a contraction occurs. However, the small mean difference measured in our experi-ments (0.11 mm for the fat and 0.23 mm for the abdominal muscle) is not statistically significant (p > 0.5), leading to the conclusion that the thickness of these tissues is approximately constant independently on the contraction of the uterine muscle. In general, the values of fat and abdominal muscle thick-nesses of our experiments are lower than those reported in the literature for nonpregnant women in the same age range. Dur-ing pregnancy, in fact, due to the expansion of the uterus, the subcutaneous tissues tend to stretch, especially in the region surrounding the umbilicus.
In conclusion, our results show that the proposed mathemati-cal model of the volume conductor is in agreement with human anatomy and can provide an accurate description of the EHG AP and volume conductor. Furthermore, even if the main focus of this paper is volume conductor modeling, the proposed mathe-matical description of the cellular AP, derived from striated mus-cle electromyography, resulted suitable for the scope. Further investigation might be dedicated to the advantages of integrating our volume conductor model with more complex descriptions of the myometrial cell AP generation [13], [14]. In view of the recent investigations on the guinea pig myometrium [12], possible limitations of the proposed model are the assumption
526 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 57, NO. 3, MARCH 2010
that the myometrial tissue is isotropic and the hypothesis that APs propagate exclusively either along the longitudinal or the circumferential axis of the uterus. Therefore, in the future, the role played by the complex 3-D geometrical and anatomical structures of the myometrium in the conduction of electrical activity needs to be understood and possibly integrated in the source model. Nevertheless, on the basis of our results, the pro-posed mathematical model for the potential source leads to an accurate description of the data with a limited number of pa-rameters. Therefore, it is suitable to support future studies on the mechanism of AP propagation in humans, and ultimately sustain the development of accurate noninvasive techniques for uterine contraction monitoring and preterm labor prediction.
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Chiara Rabotti was born in Florence, Italy, in 1977.
In 2004 she received the M.Sc. degree in electrical engineering from the University of Florence, Italy. Since 2005 she has been a Ph.D. student at the signal processing systems group of the Eindhoven Univer-sity of Technology in the Netherlands.
Her research concerns the characterization of the uterine activity by electrohysterography.
Ms. Rabotti is a member of the IEEE Engineering in Medicine and Biology Society.
Massimo Mischi was born in Rome, Italy, in 1973.
In 1999 he received the M.Sc. degree in electrical en-gineering at La Sapienza University of Rome and in 2004 he received the Ph.D. degree at the University of Leiden, Netherlands.
In 2000, he became a Research Assistant at the Eindhoven University of Technology the Netherlands, where in 2002 he completed a two-year Post-Master program in Technological Design, Infor-mation and Communication Technology. His work concerned the development of cardiovascular diag-nostic methods by contrast ultrasonography. Since 2007, he has been an Assis-tant Professor at the Eindhoven University of Technology. His research covers several topics in the area of biomedical signal processing.
Dr. Mischi is currently secretary of the Benelux Chapter of the IEEE Engi-neering in Medicine and Biology Society.
Lean Beulen studied Medicine at the University of Maastricht in the Netherlands
from 2003 until 2009.
During the final year of her studies she focused on gynaecology and obstetrics. In collaboration with the Technical University of Eindhoven she studied the value of the analysis of the fetal electrocardiogram and assisted in the research of the use of electrohysterography in fetal monitoring. She recently started to work within the Department of Gynaecology and Obstetrics at the M´axima Medical Centre in Veldhoven.
Guid Oei received the Ph.D. degree from Leiden
Uni-versity, Leiden, The Netherlands, in 1996. He is a Gynaecologist-Perinatologist at M´axima Medical Center, Veldhoven, the Netherlands, and Professor in Fundamental Perinatology at the Depart-ment of Electrical Engineering Eindhoven University of Technology, Eindhoven, the Netherlands. He sub-specialized in perinatology at Flinders University in Adelaide, Australia. Since 2005, he has been Dean of the MMC Academy and director of the Medical Simulation and Education Centre.
Jan W. M. Bergmans (SM’91) received the degree
of Elektrotechnisch Ingenieur, (cum laude), in 1982, and the Ph.D. degree in 1987, both from Eindhoven University of Technology, The Netherlands.
From 1982 to 1999 he was with Philips Research Laboratories, Eindhoven, The Netherlands, working on signal-processing techniques and IC-architectures for digital transmission and recording systems. In 1988 and 1989, he was an Exchange Researcher at Hitachi Central Research Labs, Tokyo, Japan. Since 1999, he has been a Professor and Chairman of the signal processing systems group at Eindhoven University of Technology, and Advisor to Philips Research. He has published extensively in refereed jour-nals, has authored a book (‘Digital Baseband Transmission and Recording, (Kluwer, 1996), and holds around 40 U.S. patents.
